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I am not sure how to best formulate this question, but see the title? What physical reason (or what equation can I look at) to see that, at high temperatures, all the electrons will oscillate with the same frequency? (and hence make Einstein's model the correct one).

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  • $\begingroup$ Because at a high enough temperature you need to treat the optical phonon branches reasonably well, since they will be more highly populated than the Debye model assumes. $\endgroup$ – Jon Custer Jul 21 '15 at 20:04
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    $\begingroup$ The Einstein model does not describe the heat capacity due to electrons but due to lattice vibrations! Another reason (apart from optical phonons) is, that it works sufficiently well for acoustic phonons at high temperature (The Debye and Einstein models give the same curve from at higher temeperature, at $T \gg T_D$ they both give the Dulong-Petit result). $\endgroup$ – Sebastian Riese Jul 22 '15 at 8:28

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